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Math Help - quick derivative question

  1. #1
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    quick derivative question

    how would you differentiate

    x^pi

    and

    x^(pi)^2 + (pi^2)^x

    thanks...
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mathlete View Post
    how would you differentiate

    x^pi

    and

    x^(pi)^2 + (pi^2)^x

    thanks...
    The first one is easy:
    \frac{d}{dx} \left ( x^{\pi} \right ) = \pi x^{\pi - 1}

    The second is a bit harder, and I need you to clarify something: The first term is \left ( x ^{\pi} \right ) ^2 or x^{\pi ^2}?

    The derivative of the second term is "simple." The formula is somewhat ugly, but there is one:
    \frac{d}{dx} \left ( a^x \right ) = ln(a) \cdot a^x.

    -Dan
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  3. #3
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    the first term in the second part is x to the pi^2
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  4. #4
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    Quote Originally Posted by topsquark View Post
    The first one is easy:
    \frac{d}{dx} \left ( x^{\pi} \right ) = \pi x^{\pi - 1}

    The second is a bit harder, and I need you to clarify something: The first term is \left ( x ^{\pi} \right ) ^2 or x^{\pi ^2}?

    The derivative of the second term is "simple." The formula is somewhat ugly, but there is one:
    \frac{d}{dx} \left ( a^x \right ) = ln(a) \cdot a^x.

    -Dan
    thanks...i figured it out

    for the first term i just used the power rule and got

    pi^2x^(pi^(2)-1)+ln(pi^2)(pi^2)^x

    and that was right...so thanks again
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